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Despite the initial success of extensive efforts to reduce phosphorus (P) loading to Lake Erie as a part of the Great Lakes Water Quality Agreement, Lake Erie appears to be undergoing a re-eutrophication and it is plagued by harmful algal blooms. To offer insights into potential lake responses under differing Maumee River loads and reveal recent changes with time, we explored patterns in phosphorus and chlorophyll a data from 2008 to 2018 collected in western Lake Erie near the mouth of the Maumee River. We found high, but relatively stable Maumee River and lake concentrations of total P (TP) and soluble reactive P (SRP) with no discernable annual or seasonal patterns. Maumee spring TP load was not strongly related to lake TP, and lake SRP concentrations were positively but weakly related to SRP loads. Lake TP was a strong predictor of chlorophyll a, but the relationship was weaker at sites closer to the Maumee. These results highlight spatial differences both in P concentration and the relationship between TP and chlorophyll a, and these indicate that spring phosphorus loads are a weak algal biomass predictor in the portion of the western basin of Lake Erie represented by these sampling stations.

The implications of Stein's paradox stirred considerable debate in statistical circles when the concept was first introduced in the 1950s. The paradox arises when we are interested in estimating the means of several variables simultaneously. In this situation, the best estimator for an individual mean, the sample average, is no longer the best. Rather, a shrinkage estimator, which shrinks individual sample averages toward the overall average is shown to have improved overall accuracy. Although controversial at the time, the concept of shrinking toward overall average is now widely accepted as a good practice for improving statistical stability and reducing error, not only in simple estimation problems, but also in complicated modeling problems. However, the utility of Stein's insights are not widely recognized in the environmental management community, where mean pollutant concentrations of multiple waters are routinely estimated for management decision-making. In this essay, we introduce Stein's paradox and its modern generalization, the Bayesian hierarchical model, in the context of environmental standard compliance assessment. Using simulated data and nutrient monitoring data from wadeable streams around the Great Lakes, we show that a Bayesian hierarchical model can improve overall estimation accuracy, thereby improving our confidence in the assessment results, especially for standard compliance assessment of waters with small sample sizes.

Dreissenid mussels were first documented in the Laurentian Great Lakes in the late 1980s. Zebra mussels (Dreissena polymorpha) spread quickly into shallow, hard-substrate areas; quagga mussels (Dreissena rostriformis bugensis) spread more slowly and are currently colonizing deep, offshore areas. These mussels occur at high densities, filter large water volumes while feeding on suspended materials, and deposit particulate waste on the lake bottom. This filtering activity has been hypothesized to sequester tributary phosphorus in nearshore regions reducing offshore primary productivity. We used a mass balance model to estimate the phosphorus sedimentation rate in Saginaw Bay, a shallow embayment of Lake Huron, before and after the mussel invasion. Our results indicate that the proportion of tributary phosphorus retained in Saginaw Bay increased from approximately 46-70% when dreissenids appeared, reducing phosphorus export to the main body of Lake Huron. The combined effects of increased phosphorus retention and decreased phosphorus loading have caused an approximate 60% decrease in phosphorus export from Saginaw Bay to Lake Huron. Our results support the hypothesis that the ongoing decline of preyfish and secondary producers including diporeia (Diporeia spp.) in Lake Huron is a bottom-up phenomenon associated with decreased phosphorus availability in the offshore to support primary production.

Great Lakes water levels have fluctuated over thousands of years. High water levels were a problem in the 1980s, but a recent sudden drop in Lakes Michigan and Huron has caused particular concern, in part because lower water levels are consistent with many global climate change scenarios. We examined water level data (1860–2006) representing Lakes Michigan and Huron to evaluate changes in both long-term and seasonal patterns over time, and explore relationships with candidate predictor variables. Our tools for this analysis included both Seasonal Trend decomposition using Loess (STL), and dynamic linear models (DLM). In addition to the recent decline, STL results reveal a sustained decline around 1900, a long-term periodicity of ∼30 years, and an unexpected correspondence with sunspot activity. DLM results indicate a relationship with precipitation over a three-year lagged period, which has been essentially unchanging from 1900 to present. Additionally, the DLM highlights an underlying lake level decline ...

The Florida Everglades, a wetland of international importance, has been undergoing a significant shift in its native flora and fauna due to excessive total phosphorus (TP) loadings (an average of 147 t per annum from 1995to 2004) and an elevated mean TP concentration (69 microg L(-1) of TP in 2004) from agricultural runoff and Lake Okeechobee outflow despite the use of 16000 ha of stormwater treatment areas. Here, we present a Bayesian changepoint analysis of long-term experimental research and show that exceeding a surface water geometric mean TP threshold concentration of 15 microg L(-1) causes an ecological imbalance in algal, macrophyte, and macroinvertebrate assemblages as well as slough community structure. A phosphorus threshold for all trophic levels may be more realistic and protective when presented as a threshold zone (12-15 microg L(-1)) because estimates of uncertainty must be utilized to accurately define TP thresholds, which change with seasons and water depths. Most interior areas of the Everglades are currently at or below this threshold zone, but the exterior areas near inflow structures (except for the Everglades National Park) are presently receiving double or triple the proposed threshold. Our Bayesian approach, used hereto address ecological imbalance along nutrient gradients, is applicable to determining thresholds and stable states in other aquatic ecosystems.

The northwestern Gulf of Mexico shelf has been nicknamed "The Dead Zone" due to annual summertime (May-September) bottom-water hypoxia (dissolved oxygenor =2 mg L(-1)) that can be extensive (20 000 km2) and last for several months. Hypoxia has been attributed to eutrophication caused by increasing nitrogen loads, although directly linking hypoxia to nitrogen is difficult. While the areal extent of hypoxia has been shown to increase with Mississippi River flow, it is unclear whether this increase results from enhanced vertical water-column stratification or from eutrophication caused by river-borne nutrients. Disentangling the relative contributions of eutrophication versus stratification has important management consequences. Our analysis indicates that the top:bottom salinity difference is an important predictor of hypoxia, exhibiting a threshold, where the probability of hypoxia increases rapidly, at approximately 4.1 ppt. Using a Bayesian change-point model, we show that this stratification threshold decreased from 1982 to 2002, indicating the degree of stratification needed to induce hypoxia has gone down. Although this declining threshold does not link hypoxia and nitrogen, it does implicate a long-term factor transcending yearly flow-induced stratification differences. Concurrently, we show that surface temperature increased, while surface dissolved oxygen decreased, suggesting that factors in addition to nitrogen may be influencing the incidence of hypoxia in the bottom water.

Integrated control of both point and nonpoint source water pollution using Total Maximum Daily Load (TMDL) assignments will be a major regulatory focus over the next decade. We propose the use of "flow-adjusted" pollutant concentrations to evaluate the effectiveness of management actions taken to meet approved TMDLs. Pollutant concentrations are usually highly correlated with streamflow, and flow is strongly weather-dependent. Thus, pollutant loads, which are calculated as pollutant concentration multiplied by streamflow, have a large weather-dependent variance component. This natural variation can be removed by calculating flow-adjusted concentrations. While such values are not a direct measure of pollutant load, they make it easier to discern changes in streamwater quality. Additionally, they are likely to be a better predictor of pollutant concentrations in the receiving waterbody. We demonstrate the use of this technique using long-term nutrient data from the Neuse River in North Carolina. The Neuse River Estuary has suffered many eutrophication symptoms, and a program to reduce nutrient loading has been in place for several years. We show that, in addition to revealing recent reductions in nutrient inputs, annual flow-adjusted riverine nutrient concentrations show a more pronounced relationship with estuarine nutrient concentrations than do annual nutrient loads. Thus, we suggest that the calculation of flow-adjusted concentrations is a useful technique to aid in assessment of TMDL implementation.

To address the impaired condition of the water bodies listed under Section 303(d) of the Clean Water Act, over 40 000 total maximum daily loads (TMDLs) for pollutants must be developed during the next 10-15 years. Most of these will be based on the results of water quality simulation models. However, the failure of most models to incorporate residual variability and parameter uncertainty in their predictions makes them unsuitable for TMDL development. The percentile-based standards increasingly used by the EPA and the requirement for a margin of safety in TMDLs necessitate that model predictions include quantitative information on uncertainty. We describe a probabilistic approach to model-based TMDL assessment that addresses this issue and is suitable for use with any type of mathematical model. To demonstrate our approach, we employ a eutrophication model for the Neuse River Estuary, North Carolina, and evaluate compliance with the state chlorophyll a standard. Any observed variability in chlorophyll athatis notexplained bythe model is explicitly incorporated via a residual error term. This probabilistic term captures the effects of any processes that are not considered in the model and allows for direct assessment of the frequency of standard violations. Additionally, by estimating and propagating the effects of parameter uncertainty on model predictions, we are able to provide an explicit basis for choosing a TMDL that includes a margin of safety. We conclude by discussing the potential for models currently supported by the EPA to be adapted to provide the type of probabilistic information that is necessary to support TMDL decisions.

We determined PCB congener concentrations in coho and chinook salmon collected in two Lake Michigan tributaries during the fall of 1996. Chinook salmon were larger than coho salmon and contained higher concentrations of the 78 PCB congeners we detected. There were no differences between male and female chinook or coho salmon in size or their PCB concentrations. Among individual fish, we found little evidence for a relationship between congener concentrations and percent lipid; however, congener concentrations did show a generally positive relationship with salmon size. Fish and macroinvertebrate congener concentrations are clearly related, and PCB congeners biomagnify approximately 20-30-fold as they flow from macroinvertebrates, two trophic levels below salmon, to the salmon. Slopes of regressions of salmonid congener concentrations on macroinvertebrate congener concentrations within homologs indicated that the degree of biomagnification generally increased with the degree of congener chlorination, although this pattern was much stronger for Mysis than for Diporeia. Log Kow and categorical variables for coplanar and "toxic" PCBs were not significant additional model terms, indicating that bioaccumulation of PCB congeners was not statistically related to these physicochemical attributes of the PCBs. The distribution of homologue PCBs shifts from a distinct predominance of hexachlorobiphenyls in macroinvertebrates to pentachlorobiphenyls and hexachlorobiphenyls in the salmon.

The Neuse River Estuary in North Carolina has recently received considerable public attention for severe algal blooms, large fish kills, and outbreaks of toxic microorganisms. To investigate the belief that nutrient enrichment has worsened in recent years, we analyzed long-term and seasonal trends in nutrient concentrations along the river and estuary employing seasonal trend decomposition using local regression analysis (STL). The nonparametric nature of the STL approach makes it possible to identify nonlinear trends and seasonal interactions that would be missed by traditional trend detection methods. The results indicate that while there may have been minor increases in nitrogen concentrations at upstream locations over the past twenty years, those changes are not reflected in the lower river and estuary. However, the pronounced decreases in phosphorus concentrations that occurred upstream, corresponding to a phosphorus detergent ban in 1988, do persist downstream. The net result is that the ratio of n...

The state of Wisconsin has recently issued a fish consumption advisory that includes suggested consumption rates for Lake Michigan fish, based on fish size and PCB concentration. To evaluate the size-based exposure risk from Lake Michigan fish consumption, we estimated PCB exposure probabilities for five Lake Michigan fish species using two Bayesian models. The models confirm that very few individuals of any of the five species are likely to have PCB concentrations low enough to fall into the category in which consumption is unrestricted. Among smaller fish ( 60 cm). Eating meals from multiple individuals of some species results in a high probability that at least one of the meals will exceed 1.9 mg/kg, the upper PCB concentration recommended for consumption in the advisory.

I examined 20 years of PCB concentration data from five species of Lake Michigan fish. Species-aggregated plots of corrected PCB concentration versus time indicate that PCB levels have remained fairly constant since the early 1980s. Species differences in PCB levels occur with lake and brown trout exhibiting relatively high levels and rainbow trout exhibiting the lowest concentrations. PCB concentration differences with location were also discernible in all species. However, PCB concentration data corrected for the effects time, length, location, and interspecies variability show no relationship with percent lipid content, contrasting the results of previous researchers. These observed relationships provide potential tools for managers to exploit to effectively lower human PCB exposure from the consumption of Great Lakes fish.

We have developed individual-based models that describe PCB accumulation and variability in Lake Michigan coho and chinook salmon. The models are based on simplified allometric relationships and incorporate a minimum of free parameters. Simulations of high and low growth rates demonstrate that salmon of a given age attain similar PCB concentrations but very different sizes, indicating that age is a better predictor of contaminant level than is size. Model results suggest that a 10-11% reduction in PCB levels for fish of a given size can be obtained by managing for high growth rates. The models also show that prey PCB concentration strongly affects PCB levels in the salmon; however, management options for controlling prey PCBs are fairly limited and expensive